by Maria Puente, USA TODAY

by Maria Puente, USA TODAY

Will and Kate's royal show must go on, topless photos notwithstanding.

Prince William and his wife Catherine, the Duke and Duchess of Cambridge, set off this week for four days of public engagements in London and in the north of England, taking to heart the royal imperative to carry on no matter what.

It's their first public foray since their tour last month of Southeast Asia and the South Pacific, an otherwise rousing 10-day success nearly spoiled by an embarrassing scandal over topless pictures of the duchess published in a French magazine, on the Internet and in other European publications.

In the U.K., however, it's barely a scandal and unlikely to cause long-term damage to the couple, both 30, or to the royal family. Most people, including the nastiest tabloids, take their side. "A storm in a teacloup," says Claudia Joseph, a Daily Mail reporter and biographer of the duchess.

"People really don't care in the U.K.," adds Dickie Arbiter, a royal commentator and former press secretary to Queen Elizabeth II.

The rest of the world will be watching this week as the couple take on typical royal tasks - planting trees, visiting parks, opening a sports center, meeting with students and addicts, and schmoozing with philanthropists at a gala dinner. What matters is not what they do, but how they look doing it. Do not expect them to be tense and unhappy.

"It's going to be business as usual, carrying on doing their job," says Arbiter. Even after learning about the pictures midway through their tour, "they carried on behaving as if nothing had happened and got into the spirit of everything."

People's royals correspondent Simon Perry, who was on the tour with them, confirms that. On the first afternoon after the pictures were published, he says, William looked stern and Kate had her hand on his back, as if to support him. He says the uproar may turn out to be beneficial to her image.

"She showed a so-far-unseen part of her character. ... She was stoical and strong," Perry says. "My impression is that she would not have wanted it to happen, but she seems able to cope with what might be seen as the bad side of fame."

The duchess gained new respect by the way she handled herself, says royals biographer and historian Hugo Vickers. "I am sure that their next engagements will show the same spirit," he says.

With the backing of the royal family, William is pursuing civil and criminal cases against the French magazine Closer and the so-far-nameless paparazzo who snapped the couple sunbathing in Provence just before they embarked on their tour on behalf of his grandmother, the queen.

His lawyers have won an injunction against the magazine, banning it from publishing more pictures, and he would like to see the photographer jailed under French privacy laws. Nevertheless, the injunction applies only in France, and, so far, an Irish newspaper and Italian, Danish and Swedish magazines have published even more pictures of the future queen, the former Kate Middleton.

But not in the U.K. media, which fears the British government may try to pass a strict privacy law like the one in France, Arbiter says. Although even more embarrassing photos of Prince Harry totally nude in a Las Vegas hotel room were published this summer in the U.K., in the USA and across the Internet, last week the royals decided not to pursue a U.K. complaint about the bare shots of the third-in-line to the throne.

"It's impossible to pursue because Harry invited guests into his room," Arbiter says. The Cambridges, by contrast, were staying at a cousin's private chateau, and the blurry pictures were taken from a public road hundreds of yards away.

Even more important, the topless-Kate uproar is the perfect storm of William's fears that his wife would be victimized by the paparazzi. He has not forgotten how his mother, Princess Diana, was hounded during her time as Princess of Wales, and he continues to blame them for her death in a 1997 Paris car crash involving a drunken driver.

"William is very protective of Kate," says Joseph.

And he's furious because his wife's privacy was invaded, Arbiter says. "For something like this to happen almost 15 years to the day (after Diana's death) has made made him incredibly angry, so he's using the law, which is there (in France) to protect individuals, not just princes."

One thing all agree on: "Kate has learned lessons from this experience and won't sunbathe topless again," Joseph says.

Here's what Will and Kate will be doing this week:

Monday: Meet with law-student scholars at Middle Temple in London.

Tuesday: To Burton-on-Trent in Staffordshire to open a football center.

Wednesday: To Newcastle-upon-Tyne, Stockton-on-Tees to meet with students, Olympic volunteers, social workers and recovering addicts.

Thursday: He goes to a dinner for one of his charities, 100 Women in Hedge Funds Philanthropic Initiatives.